Second, cultivate students' interest in learning and discuss exercises in depth. Mathematics is a bilateral activity, and only teachers teach without students, which will only lead to natural and ineffective. It is the key to fully mobilize students' subjective initiative and mobilize students to cooperate with teachers in class. Through the guidance of teachers and students' practice, students discuss with each other and strengthen the discussion, induction and summary of problems.
Third, let students learn the basic methods to solve problems. Junior high school usually has comprehensive method, analytical method and reduction to absurdity. Using comprehensive method to solve problems, considering problems from known conditions, and gradually deducing the unknown; Using analytic law, starting from unknown conditions, the known conditions needed to solve the problem are gradually deduced, and the road from known to unknown is explored. These two methods are generally used when the subject conditions are few and the difficulty is low. For more complex and comprehensive topics, we should learn to analyze and synthesize, and at the same time seek ways to solve problems according to known and unknown conditions, which is the so-called analytical synthesis method. There are solutions to problems, but there are no fixed methods to deal with various problems. Don't memorize all kinds of solutions, but cultivate your analytical ability, be good at analyzing the characteristics of all kinds of problems, explore solutions according to the characteristics of problems, and accumulate experience in solving problems.
Fourth, teach students to pay attention to the accumulation of problem-solving skills. Some difficult problems generally need some treatment before they can be solved by using the relevant knowledge of books. For example, the auxiliary line problem in geometry is usually combined with theorems, and the problem-solving skills of different theorems are different. For another example, if algebra students don't understand and memorize some problem-solving skills, even if they are familiar with conceptual theorems and formulas, it is difficult to use them and they can only solve some basic problems. Therefore, to do a good job in difficult questions, it is necessary to take notes on technical questions, so as to deepen the understanding of various questions.
Fifth, cultivate students' good thinking habits and consolidate knowledge through practice. The rigor of thinking is an important aspect of thinking ability. If you don't think carefully when solving problems, you will lose sight of one thing and hinder the further improvement of mathematics level. Many students always think that they know how to solve problems but can't, so they feel stupid and have poor understanding ability, but they don't look for reasons from their own learning methods. Knowledge is hierarchical and has not reached the level of flexible application. Therefore, there is nothing we can do when we meet some unfamiliar topics. To truly master knowledge, it is necessary to consolidate it through appropriate exercises, find out the connotation and extension of knowledge, and then link it with the relevant knowledge learned in the process of solving problems, and then conceive the thinking method of solving problems, accumulate different types of experience in solving problems at ordinary times, and improve the efficiency and accuracy of solving problems in exams, so as to be handy.
In short, to improve students' problem-solving ability, we must remember the basic knowledge-applying exercises-comprehensively consolidating and improving-summarizing methods and skills, improving sublimation, having the spirit of research and determination, refining problem-solving methods, accumulating problem-solving experience and improving problem-solving efficiency.